Representability of locally compact regular spaces by domains and formal spaces

✍ Scribed by Inger Sigstam; Viggo Stoltenberg-Hansen

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 850 KB
• Volume: 179
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(96)00152-1

✦ Synopsis

When computing on a (generally) uncountable topological structure d, such as the topological field of real numbers R, one must by necessity compute on a set of concrete approximations P for d. One way to do this is to represent the original structure d using P in such a way that computations on P transfer to approximate computations on d. Two such representations are considered, domain representability and representability by formal spaces, and these are compared for the class of locally compact regular spaces. It is shown that for locally compact regular spaces the two representations are equivalent over P for natural sets of approximations P. In addition it is shown that under rather general conditions, a continuous function between topological spaces represented by formal spaces over PI and 4, respectively, lifts to a continuous function between the corresponding domains, the ideal completions of PI and P2.